Something I quickly wrote for you - so could be cleaned up. Check if this helps:
String string = "02/01/2014"; //assuming input
DateFormat sdf = new SimpleDateFormat("MM/dd/yyyy");
Date dt = sdf .parse(string);
Calendar c = Calendar.getInstance();
c.setTime(dt);
c.add(Calendar.MONTH, 1); //adding a month directly - gives the start of next month.
String firstDate = sdf.format(c.getTime());
System.out.println(firstDate);
//get last day of the month - add month, substract a day.
c.add(Calendar.MONTH, 1);
c.add(Calendar.DAY_OF_MONTH, -1);
String lastDate = sdf.format(c.getTime());
System.out.println(lastDate);